Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22553519 | C2 | semidirect |
| 4. #22553058 | C2 | semidirect |
| 5. #22553044 | C2 | semidirect |
| 7. #500×C131 | C2 | semidirect |
| 55. D524 | Q16 | semidirect |
| 92. C131 | #1649 | semidirect |
| 95. #500 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553977 | 2 |
| #22553589 | 2 |
| #22553519 | 2 |
| #22553058 | 2 |
| #22553044 | 2 |
| #22553041 | 2 |
| #500×C131 | 2 |
| #1649 | 131 |